How do we measure genetic variation?

A locally interbreeding group within a geographic population is called a Mendelian population. Mendelian populations are often the subjects of evolutionary studies. To measure genetic variation in a Mendelian population precisely, we would need to count every allele at every locus in every individual in it. By doing so, we could determine the relative proportions, or frequencies, of all alleles in the population. Fortunately, we do not need to make such complete measurements, because we can reliably estimate allele frequencies for a given locus by counting alleles in a sample of individuals from the population. The sum of all allele frequencies at a locus is equal to 1, so measures of allele frequency range from 0 to 1. An allele’s frequency is calculated using the following formula:

p = number of copies of the allele in the population

sum of alleles in the population

If only two alleles (for example, A and a) for a given locus are found among the members of a diploid population, they may combine to form three different genotypes: AA, Aa, and aa. Using the formula above, we can calculate the relative frequencies of alleles A and a in a population of N individuals as follows:

- Let NAA be the number of individuals that are homozygous for the A allele (AA).

- Let NAa be the number that are heterozygous (Aa).

- Let Naa be the number that are homozygous for the a allele (aa).

Note that NAA + NAa + Naa = N, the total number of individuals in the population, and that the total number of copies of both alleles present in the population is 2N because each individual is diploid. Each AA individual has two copies of the A allele, and each Aa individual has one copy of the A allele. Therefore, the total number of A alleles in the population is

2NAA + NAa. Similarly, the total number of a alleles in the population is 2Naa + NAa. If p represents the frequency of A and q represents the frequency of a, then

2N_AA+N_Aa

P=---------

2N

fnd

2Naa +N_Aa

q =---------

2N

To show how this formula works, calculates allele frequencies in two populations, each containing 200 diploid individuals. Population 1 has mostly homozygotes (90 AA, 40 Aa, and 70 aa); population 2 has mostly heterozygotes (45 AA, 130 Aa, and 25 aa). The calculations demonstrate two important points. First, notice that for each population, p + q = 1. If there is only one allele in a population, its frequency is 1. If an allele is missing from a population, its frequency is 0, and the locus in that population is represented by one or more other alleles. Since p + q = 1, then q = 1 – p. So when there are only two alleles at a given locus in a population, we can calculate the frequency of one allele and then easily obtain the second allele’s frequency by subtraction. The second thing to notice is that both population 1 (consisting mostly of homozygotes) and population 2 (consisting mostly of heterozygotes) have the same allele frequencies for A and a. Therefore, they have the same gene pool for this locus.

However, because the alleles in the gene pool are distributed differently, the genotype frequencies of the two populations differ. Genotype frequencies are calculated as the number of individuals that have the genotype divided by the total number of individuals in the population. In population 1 in Figure, the genotype frequencies are 0.45 AA, 0.20 Aa, and 0.35 aa. The frequencies of different alleles at each locus and the frequencies of different genotypes in a Mendelian population describe its genetic structure. Allele frequencies measure the amount of genetic variation in a population; genotype frequencies show how a population’s genetic variation is distributed among its members. With these measurements, it becomes possible to consider how the genetic structure of a population changes or does not change over generations.